Cooperation, Relationship, and Evolutionary Process in Institutions 1

Transcription

1 Cooperation, Relationship, and Evolutionary Process in Institutions 1 Xie zhigang Visiting Research Fellow International and Asian Research Group Japan Center for Economic Research (JCER) Assistant Researcher Institute of Economic Research Chinese Academy of Social Sciences (CASS) Abstract A synthesis of theoretical analysis on cooperation in games, institutional evolution framework and comparative analysis of institutional divergence is proposed to explain how cooperation is emerged and sustained, how institutions related to cooperation pattern evolve. Firstly, this study attempts to connect cooperative behavior in a repeated trust game in social network with consideration of a trust threshold on the relationship. Secondly, the interaction and co-evolution of formal/informal institutions are analyzed through a conceptual framework synthesizing a subjective modification of the model with the Hayekian Spontaneous Order thoughts. Finally, the deviation between formal/informal institutions in the framework is employed to explain the institutional diversities in cases of China, Japan and the US. Keywords: social dilemma, trust game, formal/informal institutions, spontaneous order 1 This research is supported by Nikkei Asia Scholarship and Japan Center for Economic Research (JCER). I sincerely thank to the staff at the International and Asian Research group at JCER for all the supports. 1

2 1. Introduction Institutional divergence on cooperation pattern Cooperation in human society, being famous as the social dilemma, attracts great attention in the fields of sociology, politics, and economics recently. In a social dilemma, individually reasonable behavior leads to a situation in which cooperation doesn t rise and everyone is worse off. A central question in social dilemma is how cooperation is emerged and sustained. As the connections between cooperation, culture and institution being recognized, further questions arise: What institutions make cooperation on such a large scale possible? Why there is institutional divergence on cooperation pattern? What is the culture and institution co-evolutionary dynamics? Aiming to these questions in social dilemma, this paper proposes a synthesis of theoretical analysis on cooperation in games, institutional evolution framework and comparative analysis of institutional divergence in a formal and informal institutional evolution perspective. There are lots of arguments for and against the institutional convergence in globalization. The consciousness of cultural differences among the peoples of the world is obvious. However, when consider the institutional system incorporating the two levels, namely formal and informal institutions, debates rise. Some scholars argue that the cultural differences, especially in beliefs, values, attitudes and norms between the West and the East, may create tensions and misunderstanding, even conflicts. Samuel Huntington, in his well-known The Clash of Civilization (1993), warns of the future challenges of Confucian and Islamic cultures to the West. In contrast to this view, Francis Fukuyama (1992) declaims that since the fall of communism in Eastern Europe that ended the Cold War in 1990, the post-cold War era represents The End of History. From an institutional evolution perspective, both The End of History and The Clash of Civilizations are doubtful hegemonic discourses due to the confusion of multiple levels of institutions. There are two inconsistent trends of institutional evolution process, the rule of laws on the formal level, versus culture, norms and values on the informal level. To better understand the coevolution of formal/informal institutions, this study employs a repeated trust game played in a social network, in which captures the cooperate threshold on social ties as the core of informal institution, and synthesizes a subjective modification of the model with the Hayekian Spontaneous Order thoughts to a conceptual framework on institutional analysis. The paper is organized as following. Firstly, related theories and methods are discussed in the following section. A core function of culture and norms, referring as informal institution in this study, is to solve the problem of social dilemma in which reasonable individual does not cooperate even cooperation result in better off.in dealing with cooperation behavior patterns in society, various ideas and method are presented. Three main approaches are provided to explain the emergence of cooperation in the Prisoner s Dilemma. Firstly, an exogenous agent or formal institution, which monitors and punishes the defection behavior of interactions among individual, is introduced into the situation. However, it does not explain the spontaneous emergence of cooperation without law and government. In order to improve the explanation, the conception of 2

3 social preference or reciprocity, which is motivated by recent research in the fields of sociology and psychology and neural science, is employed to solve the social dilemma. Obviously, there is a foundational conflict of the assumptions between reciprocity and rationality in economics. The third optional method is to emphasis the positive effect of social networks on facilitating collective action. In specific social structure, cooperation pattern can be explained with social-learning process, reputation and information system. Secondly, a formal repeated trust game model is proposed to analysis the cooperate pattern in social network. The present model provides an alternative and universal understanding of cooperate behavior pattern through incorporating social ties theory with setting threshold parameter on relationship as social preference instead of reciprocity. Thirdly, subjective decision-making approach is employed to modify the static game model, and Hayekian Spontaneous Order or extended order of human cooperation thoughts is expressed in the conceptual framework. To better understand the divergent institutional evolution process of the real world, subjective decision-making approach is employed to extend the trust game model. In the conceptual framework inspired by Hayekian thoughts of Extended Order of Human Cooperation, formal institution dose not determine informal institution rigidly, but affects informal institution primarily because of the deviation of individual subjective assessment on the trust level and function of formal institution in society. Finally, the institutional divergence of China, Japan and US is discussed as cases. In doing so, the paper employs game-theoretic reasoning and interpretations of divergent institutional evolution between China and Japan, which also clarifies the simplicity of prevailing arguments that identify East Asian developmental and institutional features with authoritarianism, collectivism, kinship-dominance, Confucianism and the like. In contrast to these opinions of unique pattern of the East, such as the Guanxi and Fei s the Differential Mode of Association theories, the trust game in social network presented in this paper offered an alternative perspective on trust and cooperation. Differentiate trust and cooperation patterns can be explained in this analysis in a general way without defining a distinctive oriental mode to the west. By constructing a trust game model in which agents cooperate based on the relationship in social network and an individual threshold parameter, cooperation is explained in a universal way. It captures the realistic feature of cooperation among individuals in social ties, and explains the diversities of the East and the West with the difference of formal institutions. 3

4 2. Related theories and methods Social dilemma and cooperation In recent years, a great amount of scholarly attention in politics, sociology and economics, has been devoted to the puzzle of emergence of cooperation in society. A central question in interdisciplinary literature of cooperation is how to solve the social dilemma. From a game-theoretical perspective, social dilemma is game in which individual and collective interests conflict. Economists have studied cooperation as a problem of trust using various forms of games. The simplest is the familiar two-person Prisoner s Dilemma game. The N-player Prisoner s Dilemma, of which the Prisoner s Dilemma Game is a special case, describes the cooperation problem in generalities (Dawes, 1973; Hamburger, 1973). Repeated games are proposed to solve the cooperation problem. In those games, self-interested players sustain cooperation not because they care about others, but because they try to maximize their own gains over time (Fudenberg and Maskin,1986; Kandori, 1992; Tirole, 1996). New economic institutionalists have emphasized a rule-oriented definition of institutions in which these are the way a game is played. Binmore and Samuelson (1992) point out, whenever cooperation is not an equilibrium, it may be attained by means of the introduction of institutional arrangements that allow to coordinate the outcomes of the players. If multiple equilibria arise in a game, specific institutions define its outcome. If collective processes involve repeated PD-type games individuals face a potential coordination failure, that is, the optimal, or Pareto-efficient, situation may not be achieved due to a lack of institutional mechanisms within the game that shift the players into a more cooperative solution. To reach superior collective situations arrangements need to be introduced in the game. The attainment of efficiency may be done in different ways. When considering a one-shot static game different behavioral assumptions may help in enlarging the strategy sets and in achieving outcomes Pareto preferred. If the game is considered to be played for more than one period individual strategic decisions may lead to Pareto improvements. Institutions are incorporated in game as a device to avoid the inefficiency of non-cooperative equilibrium. Greif (1989, 1993) and Milgrom et al. (1990) model a large number of traders who are randomly paired with each other in each period. Each pair agents play the trust game where one party has an incentive to cheat the other by supplying goods of inferior quality. It is argued that the exchange of information on the identity of cheaters or the development of a mechanism which strengthens the power of enforcement can help to sustain cooperation. Kandori (1992) shows that sustain cooperation in Prisoner s Dilemma may be possible in a sequential equilibrium if all individuals employ the contagious strategy in which agents who have not experienced a defection choose cooperation, and agents who have experienced a defection choose defection. Ellison (1994) introduces a public randomization punishment device into the contagious equilibrium which applies to more general payoff structures. More recently, Dal Bó (2007) shows how random matching and a community enforcement mechanism can support unequal caste-type systems among identical agents that would not be sustainable under 4

5 the standard two-agent fixed-matching protocol. C D C R,R S,T D T,S P,P Table 1. Generalized Representation of the Prisoner s Dilemma Follow the standard labels originally introduced by Rapoport and Chammah (1965), Table 1 demonstrates the simplest form of the Prisoner s Dilemma. In the table, C notes Cooperation, D notes Defection, and in the payoffs, R is the Reward from successful cooperation, S is the Sucker s payoff, T is the Temptation payoff, and P is the Punishment for defection. In discussion of social dilemma and cooperation, the elements of the payoff matrix satisfy the conditions: T > R > P > S and 2R > (T + S). These conditions imply that defection is good for one individual but mutual defection leads to the second worst result. In this original prisoner s dilemma game, players can make two choices: cooperate or defect, and they get payoff depending on their choices. The prediction of the model showing in Table 1 is quite straightforward. The prisoner s dilemma is dominance solvable. It has a unique equilibrium in pure strategies. Both players defect from the outset. This even holds if the game is repeated, provided its end is defined (Selten 1978; Rosenthal 1981). In recent years, there has been an important shift in game theory away from classical solution concepts such as Nash equilibrium, and towards evolutionary game theory solution concepts such as the evolutionary stable strategy and the replicator equations. Evolutionary game theory is an extension of the classical paradigm towards bounded rationality. An evolutionary game (Firedman,1991) is a dynamic model of strategic interaction with change in gene frequency in populations to game theory. It differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibrium. Evolutionary game theory describes game models in which players choose their strategies through a trial-and-error process in which they learn over time that some strategies work better than others. Trust game model, as an alternative to the standard Prisoner s dilemma, is employed in the evolutionary game theory regularly (Kreps 1990; Berg et al., 1995; Snijders 1996; Buskens 2002).Compared to the Prisoner s Dilemma game, the trust game, or the investment game has several features. Firstly, the trust game in which two players move sequentially is more closely related to many one-sided incentive problems in real world. Secondly, there is no strictly dominant strategy in the trust game. It allows the establishment of trust relationships among different agents with some degree of credibility. For these reasons, the trust game may be a more realistic imitation to the environment for the achievement of a social norm of cooperation than the Prisoner s Dilemma game. 5

6 Trustor(r) Not Entrust Entrust (,) Defect Trustee(e) Cooperate (,) (,) Figure 1. Standard Trust Game Figure 1 shows the basic ideal of the standard trust game model. It involves two actors, the trustor and the trustee. Games with more than two actors can be likewise analyzed. The game starts with a move of the trustor. He can choose between placing or not placing trust. If trust is not placed, the interaction ends, and if trust is placed, then trustee chooses between honoring and abusing trust. The trust game has similar payoffs structure and labels to the Prisoner s Dilemma, and it does not solve the social dilemma in the simplest form either. Using behavioral and evolutionary game theories, endogenous social preference is considered in study of social dilemma. It is argued that the actual choices of individuals in social dilemmas are strongly affected by various contextual factors, and there are a significant proportion of individuals who have non-selfish utility functions or, in other words, have intrinsic social preferences. They take into account other individuals interests as well as their own in the decisions they make. The social preference becomes a key issue in evolutionary game theoretic approach to collective action that provides a way to model the historical interaction between the institutional structures and individual (Bowles, 1998, 2000; Güth and Kliemt, 1998; Güth, Kliemt, and Peleg, 2000). Furthermore, Bowles and Gintis(2003) suggest that many humans have a predisposition to punish those who violate group-beneficial norms, even when this imposes a fitness cost on the punisher. Such altruistic punishment is widely observed to sustain high levels of cooperation in behavioral experiments and in natural settings. 6

7 Trustor(r) Not Entrust Entrust (,) Defect Trustee(e) Cooperate (,) (,+) Figure 2. Extensive form of trust game with social preference An extension of trust game showing in Figure 2 incorporates social preference of the trustee. Although in a simple form, it captures the basic logic of agents intrinsic social preferences in solving the cooperation dilemma. The subjective extra utility from cooperation changes the payoff structure of the game. Given the condition of + >, the trustee choose to cooperate instead of defect, thus cooperation equilibrium becomes sustainable. Social capital and relationships Social dilemma of trust and cooperation problem is regularly related with theory of social capital in sociology and economics literature. Most recently there has been a surge of interest in the related notion of social capital. Broadly speaking, social capital is a set of values and relationships created by individuals in the past that can be drawn on in the present and future to facilitate overcoming social dilemmas. According to Fukuyama (1999), social capital can be defined simply as an instantiated set of informal values or norms shared among members of a group that permits them to cooperate with one another. Putnam (1993, 2000) refers social capital to features of social organization, such as trust, norms, and networks that can improve the efficiency of society by facilitating coordinated actions. Annen (2002) and Henning (2002) provide formal theories of social capital that describe how the various forms and degrees of connectedness, and the reputation effect stemming from them, result in cooperative behavior by individuals who are selfishly motivated. Social network and trust are regarded as essential factor of social capital (Ahn and Ostrom,2002). Social network, in which individuals are connected with various degrees of relationships or social ties, is introduced in game analysis on cooperation in complex circumstances recently. It is argued that humans are embedded in social structures and that they choose actions taking account of the social contexts in which they live. While social networks have been of interest to sociologists for some time (Granovetter, 1973; Coleman, 1988; Wasserman and Faust, 1994), economists have only quite recently begun to apply them to problems in various areas. However, they have already been found especially useful in understanding problems relating to trust and cooperation problem (Greif, 1993; Rauch and Casella 2001; Ghatak, 2001). 7

8 It is generally recognized that cooperation may emerges among individuals with strong social relationship more possibly than the weak one. However, the weak ties theory of Granovetter (1973, 1985) offers an alternative insight on the issue. Granovetter argues for a distinction of social capital between strong tie which connect people within a network, and weak tie which connect across networks. Weak links are better for collecting information while strong links are important for overcoming the prisoner s dilemma and coordination. Two agents are connected through a weak link if they have few common neighbors and they are connected through a strong link if their neighbors overlap to a large extent. It is argued that the overall connectedness of a society, especially through weak ties facilitates collective action at a larger scale. Societies with high levels of embeddedness are likely to have strong ties. But strong ties without weak ones may lead to a clustered but fragmented society. Following the game theoretical analysis on trust and cooperation dilemma, this study presents a trust game model repeated in social network. Comparing to prior literatures, there are several new features lies in the model. Firstly, the present model incorporates social network and social embeddedness in a distinctive way. Instead of reciprocity and other preference assumptions, individual social preference is represented by a threshold on relationships, through which trust and cooperation is related with social ties in network. Thus the present model provides an alternative and universal understanding of cooperate behavior pattern. Secondly, distinction between the behavior of trust and cooperation is clarified in this model. There are confusions regards trust, trustworthiness and cooperation in many related works. This disagreement is largely due to the fact that investigators of trust and cooperation often treat the two concepts interchangeably. The iterated Prisoner s Dilemma game, as the most popular experimental paradigm for studying trust and cooperation, entirely conflates the two. A player in a repeated Prisoner s Dilemma, faced with the binary choice of cooperation or defection, cannot show trust for the other player without cooperating and cannot show distrust without defecting; one cannot cooperate but distrust, or trust but defect. Thirdly, the decision-making logic in this model implies an alternative explanation of cooperation pattern in real world. Specifically, the cooperation pattern in individual with family member, friend, acquaintance and stranger can get a general understanding besides theories of weak ties, ethnicity trust, and so on. This behavior pattern is useful to explain institutional divergence in expression of the Hayekian Spontaneous Order or extended order of human cooperation thoughts. 8

9 3. The model The Economy as a relational network Following Watts and Strogatz (1998) who use techniques from graph theory, most research on social network focus on the topological structure. Thus undirected and unweighted networks, in which nodes are simply connected or disconnected, are more likely to be used. However, the strength of social ties plays a key role in this analysis. An undirected but weighted network is more suitable to study the cooperation pattern based on the strength of social connections. i j In an undirected & unweighted network is the number of links between and. i ω i, i +1 ω j 1, j j In this undirected & weighted network =,while 0,+ ), 0,+ ). Figure 3. The Economy as a relational network In this analysis, economy is regarded as an undirected & weighted social network, in which individuals connected with each other by social ties (See Figure 3). Between two individuals, there might be one direct connection, or several indirect connections. For two directly connected nodes, the strength of the social tie between them is measured with the weight value of the link. In this case, ω is defined as the distance in social relationship between two directly connected nodes, and is defined as the length of the shortest path between two random nodes, regardless of whether they are connected directly or indirectly. Therefore, is unique value of the social distance among each nodes pair. For two indirectly connected nodes and, the social distance between them =,while 0,+ ), 0,+ ). Suppose the social ties are chosen randomly from a probability distribution function, namely ~ ()= ( < ). 9

10 Trust game in a social network Figure 4 shows a sequential trust game in which payoffs are utilities. There are two players, the trustor takes an action before the trustee does. The parameter! in the trustee s payoff captures his subjective utilities base on the social relationship with the trustor. Being consistent with the real interaction between two individuals, trustee will gain less when defecting if he has a strong connection with the trustor. In another word, the temptation to defect will be small when two agents are in certain relationship, such as family, friend, and co-worker. Trustor(r) Not Entrust Entrust (,) Defect Trustee(e) Cooperate (,+!) (,) Figure 4. Trust game with threshold on social distance In the social network described above, a moderated trust game is randomly iterated by one trustee with " trustors in discrete time. The payoff structure is similar with that of the standard trust game. The individual subjective preference on cooperation is replaced with the social distance. The payoff of trustee is +! $ if he chose to defect. Being consistent with the real interaction between two individuals, trustee will gain less when defecting if he has a strong connection with the trustor. Consider an intermediary who inflicts punishment on defectors through the economy. There are laws and community rules that punish exploiters of others trust. If found out, the cheating payoff goes down $ because of law enforcement. The grim trigger strategies Alike to the standard trust game with the constrains of > > > and 2 > +, an one-shot game in figure 3 could only results in a prisoner s dilemma. Trigger strategies (e.g., Friedman, 1971; Baker et al., 1994; Bull, 1987; Buskens, 1998; Pearce and Stacchetti, 1998) are usually used to analyze this type of model in iterated games. Various trigger strategies can sustain an equilibrium. Trigger strategies are defined via trigger cooperative threshold θ, which indicates agent s preference on social ties. Trustor and trustee will choose to cooperate when strength of the social tie between them beyond the cooperative threshold, or. 10

11 entrust, If!!,and trustee never defect Trustor(r) not entrust cooperate, If!! and 34($) 34(6) Trustee(e) defect Figure 5. The grim trigger strategies It is important to note that social ties in the network of this model are non-directional, namely for each pairs of trustor and trustee, ( = (. On the other hand, the cooperative threshold is directional. In the decision-making framework of agent, is the criterion to choose cooperation or defection. Put in a different way, could be seen as trustworthiness of agent to agent based on the relationship between and. For instance, if! <! then the trustor has a higher preference to cooperate than that of the trustee on the same level of strength social tie. With the definition of the cooperative threshold and the distribution of social ties in the network ~ ()= ( < ), any player cooperate with another player in a probability of ( ). Because agent will cooperate with if, for a randomly chosen agent pair with the social tie of, the probability of cooperate with is ) *. Game is randomly iterated by one trustee with " trustors in discrete time + = 0,1,2. Like in the real market process, the trust game will be played infinitely. A discount factor should be added into this model to reflect the pure time preference of agents. Payoffs are depreciated exponentially with.(0. 1) for every game, and the total payoff of agent is 1 2. / 0 /. 11

12 Subgame perfect equilibrium analysis Proposition 1. In a subgame perfect equilibrium, 7! =7!, where 7! =!8,!9,!:,!; ], 7! = 8!, 9!, :!, ;! ]. Proof. According to Bellman's optimality principle in dynamic game theory(kreps, 1990), optimality on the total path is guaranteed if deviation from the prescribed path in any one decision node does not increase the payoff. Therefore, it is necessary to prove that if a player makes a one-step deviation from the equilibrium path, his payoff will decrease. Consider there exist at least one pair of trustor and trustee with!!. Firstly, assume! <!. Givern the grim trigger strategies, while having never been defected, agent either as trustor or trustee will cooperate given. In addition, agents will persist to rejection of the betrayers. In the first round, + =0: 0! =>,! <! <!,! <!!,!! <! 0! =@,! =! <!,! =!! 0,! <! <!;! =! <! 0! =>,! <!! ;! =! <! 0,!! <! ;! =!! 1 34 =C. / 0!/ 2 In the first game period + = 0, if! <! <!, the trustor can maximize his payoff in this round by setting his threshold! +D! =!. According to the grim trigger strategies adopted in this trust game, the trustor will not cooperate with the trustee in all the following rounds. In this situation, the discounted total payoffs of the trustor in all the game play with the trustee would turn to 34 1! =+ 8. /. Because of the standard assumption of >>>, the trustor gets an extra income of by changing his threshold as same as the trustee. 0, 34 = 34! <! <!;! =! <!! 34 =>,! <!! ;! =!! 0,!! <! ;! =!! 12

13 Secondly, assume! <!. When + = 0 0! =>,! <!!,! <! <!,!! <! 0! =@,! =! <!,! =!! 0! = >,! <!!;! =!! 0,! <! <!;! =! <! 0,!! <! ;! =!! In the condition of! <!!, trustor get through threshold shifting from! to!, and he can cooperate with the trustee in the rest game rounds. 1 C. / ( ) 2,! <!!;! =!! 34 =34! 34 = E 0,! <! <!;! =! <! 0,!! <! ;! =!! As > > >, then > 0, and > 0. Thus, in any condition, 34 0.Change cooperate threshold value for trustor from! to! =! is a Pareto improvement.! =! Proposition 2. Subgame perfect equilibrium exist if 7 F 8GF ( )) 7*+ +$. Proof. When! =! >!, both player defect. Given! =!!, because >, the trustor has no incentive to deviate from maximal payoff. Consider the trustee: 13

14 1 34 ($)=+C. / )()+)1 ()** /H8 =+. 1. )()+)1 ()** 1 34 (6)=+ $+C. / /H8 = + $+. 1. In equilibrium, for all! =!!, :34 ($) 34 (6). Therefore, when F ( )()+ +$, subgame perfect equilibrium exist. 8GF As, hence when F ( )()+ +$, there is : 8GF F ( )()+ +$, :3 8GF Proposition is proved. Proposition 3 There is an unique Pareto optimal subgame perfect equilibrium exits: = F 8GF ( )( )+ +$. Proof. 7! =!8,!9,!:,!; ], 7! = 8!, 9!, :!, ;! ]. 7 =7! = 7! = 8, 9, :, ; ] As 7 F 8GF ( )) 7*+ +$ is the constrain of subgame perfect equilibrium, suppose there exists a SPE KL, in which there is < for at least one. Define function: M()= F 8GF ( )()+ +$ M( ) < = M( ) Because () is the social ties distribution, M() is a monotone increasing function. Then can be increased to, and this solution is a Pareto improvement for all. Suppose there are two equilibriums 7 8 and 7 9 that do not Pareto dominate each other. 7 8 = 8 8, 9 8 ; 8 ], 7 9 = 8 9, 9 9 ; 9 ] N 8 9,1 8 < 9, < " 14

15 Define 7 : = 8 8, O, 9 OP8 9 ; ] Then N M( : ) M( 9 ),1 M( : )>M( 8 ), < " Therefore, 7 : is a SPE Pareto dominating 7 8 and 7 9. This equilibrium construction process can be repeated until the unique SPE 7 = Proposition is proved. F 8GF ( )) 7 *+ +$ appears. Proposition 4 The subgame perfect equilibrium in determined by parameters:.,,,$,. To be more specifically: SPE 7 increases with the increase of.,,$, and increases with the decrease of,. Proof. It is easy to see from the unique SPE 7 = F 8GF ( )) 7 *+ +$. According to these propositions, some basic conclusions can be acquired to explain cooperation pattern in social network. Basic conclusion 1: In the model, the trust and cooperation pattern, with which the player uses thresholds as the criterion on social distance to cooperate with others, can reach the unique subgame perfect equilibrium. Basic conclusion 2: The social cooperation level indicating with 7 is determined by external punishment on the defections in the model. Proposition 1 actually reveals the player s rational logic of trust and cooperation in the social connections. The threshold is critical for the player s well-being in the social interactions. It represents two important aspects of individual preference. Firstly in the pro-social aspect, reflects his will to cooperate with others. If is too high, the player can barely trust and cooperate with others. Secondly, if is too low, then the player may be over credulous about others, he is more likely to be defected in social interactions. Therefore, also implies the preference of aversion from betrayers. While encountering another player in social interaction, the player maximizes his payoff by setting the same threshold of the opponent. When the trust game is repeated in a random social network composed of potential future partners of transaction, the rational logic of trust and cooperation described above guarantees an unique subgame perfect equilibrium 7. This equilibrium is Pareto-optimization for every players in this game. Consequently, the 7 can be seen as the indictor for the behavior of all players, and the social cooperation level as well. 15

16 Although there are several parameters determine the 7, the external punishment on the defections $ in the model is the most important relating to the following institutional analysis in this study. The meaning of conclusion 2 is straight, social trust and cooperation level increases with the improvement of laws which confine cheating and defections. 16

17 4. Formal/informal Institution Co-evolution For analyzing the mechanism of institutional evolution, a conceptual framework, which synthesizes the basic analysis of this trust model and the extended order of human cooperation theory of Hayek is discussed in this section. Formal and informal institutions There are several different definitions of institution in game theory. Economists have regarded an institution as either a player of the game (Penard,2008), the rules of the game(north,1990), or the equilibrium outcome of game (Schotter, 1981; Greif, 1993; Aoki, 2001). In fact, the distinction and interaction between the formal and informal dimensions of social relations have long been analyzed by social theorists, particularly from the legal and sociological tradition but also by economic theorists dealing with institutions. Weber (1921) observes that the relationship between informal behavioral regularities and formal rules is complex and reciprocal. Hayek (1973, 1988) emphasizes law or moral rules that had evolved over long periods before some were eventually transformed into legislation; beneficial informal rules were principally subject to a kind of selection through cultural evolution that was neither natural nor artificial. In his analysis of institutional evolution, North (1990) stresses the distinction between formal and informal constraints, and shows aware of the central role of informal institutions, and particularly of those underpinning cultural values. Following North(1990), the law system, referring as formal institution, and tradition, culture, and norm of society, referring as informal institution, are distinguished in this study. Therefore, the conception of formal institution adheres to the first definition of institution as the rules of the game, and the term of informal institution is compatible with the second definition, the equilibrium of game. While the existence of informal institutions is well established within the new institutional literature, however, there is considerable uncertainty about how they come into existence, how they change and on the nature of the relationship between formal and informal institutions. North (1990,2001) and Williamson (2000) tend to treat culturally derived institutions as relatively permanent, changing only slowly if at all, with the result that culture then becomes an exogenous variable, albeit an important one. Informal norms of behavior come from socially transmitted information and thus constitute a part of the cultural heritage. Therefore the process of their formation and erosion must be slow and complex. The tension between politically-determined formal rules and persistent informal constraints then may have important implications for the way economies change. 17

18 Hayekian Extended Order of Human Cooperation Among theoretical viewpoints, Austrian economics distinguishes itself for highlighting the need of taking account of communication, information structures, knowledge formation and cognition. Friedrich von Hayek is a forerunner in this field. Hayek initiated a research program in which mind and society are produced by the perennial coevolution of cognition, culture and institutions. The notion of Spontaneous Order is dominant in his research on social evolution, in which norms are produced and learnt through a gradual process of trial and error. A considerable body of work of Hayek details the spontaneous order theory, such as The Constitution of Liberty (1960) and Law, Legislation and Liberty (1973). In his later work The Fatal Conceit (1988), he claims that the spontaneous order can precisely described only as the extended order of human cooperation. Hayekian Spontaneous order or Extended order of human cooperation theory shed light on institutional evolution analysis, especially on the coevolution process of formal/informal institutions. The central idea of Hayekian spontaneous order is that social orders are the unintended consequences of individual actions. From the time of Karl Menger(1871), some social phenomena like currency system and languages are noticed by Austrian economists. These phenomena are the consequence of result of human action, but not of human design. Evolved codes of law, languages, family organizations, moral rules as well as rules of conduct, are the result of this process, which gradually and tentatively selected better-fit and socially more beneficial institutions. The market with its system of property rights and legally enforceable rules, represents the best example of this evolved set of institutions. An important aspect of Hayek s work is the emergence of spontaneous orders that facilitate cooperation versus the need for the state to formally legislate rules to foster cooperation. The central question becomes the extent and robustness of governance mechanisms, their ability to handle problems of social diversity, large populations, and capacity to handle violence. The view of spontaneous order is, for Hayek, the great contribution of that tradition of thought initiated by Mandeville and Hume and continued by the Scottish moral philosophers of the eighteenth century, such as Adam Smith and Ferguson in the field of economics, and Edmund Burke in the field of political thought. Hayekian spontaneous order is an analogue to Smith s invisible hand. In the perspective of the market processes in Austrian economics, the interesting aspect of Smith is that he studied economics while considering moral philosophy and law as spontaneous emerging orders. In more contemporary terms, they focused not on how to assign scarce resources but rather on how scarce resources are spontaneously assigned (Kirzner, 1976). In the recent institutional literature, great efforts are made to translate some Hayek s insights of paradigmatic situations of social interaction and interdependency of decisions into a game-theoretic structure (Schotter,1981; Aoki,2001). Hayek s analysis of social orders offers a strong theoretical basis for a game theorist to model the way institutions form. It captures the passage of time and the experimentation process that seems to intervene in repeated games; individualism underpins the use of dominant strategies in determining equilibrium solutions; the role of knowledge may become an important tool in the selection of equilibrium and, also, in the 18

19 discovery of new equilibrium solutions. Game theory does not, and cannot, offer any model of the learning process of the players, nor therefore of the particular selecting procedure that players may adopt to choose among different equilibrium options. Game theory suffices to describe the conditions under which mutual expectations are matched, but not the process. Out-of-equilibrium moves are what they are, irrational, dominated strategies and not possible steps of a learning process where error-making and error-correcting are as informative as the final solution. Hayek s and Kirzner s idea that non-coordinated behavior informs how coordination proceeds is lost here. Subjective game framework In game theory it is customary to assume, often implicitly and sometimes explicitly, that each player has well-formed knowledge of the game he plays. As game theory developed, attempts were made to relax some of these assumptions. A newly developed subjective approach, which is named as subjective or inductive games, is established to explain the process of generation and evolution of endogenous institution (Kalai and Lehrer, 1995; Matsushima, 1998; Aoki, 2001; Feinberg, 2005; Kaneko and Kline, 2008). In these new subjective game models, prior assumptions of complete rationality and complete information are usually replaced with bounded rationality and subjective knowledge, and the form of the game is not the objective structure but a subjective cognition of the players to the objective scene. This subjective approach attempts to present a more realistic open model, where each player takes only a subjective partial view of his individual decision problem. Institutions as the outcome of game become the subjective equilibrium, and they can evolve in the history process. This repeat trust game model hereinbefore actually provides a stationary analysis of how cooperation could maintain and increase in human society. It captures a realistic generalized pattern of interaction in society, such as transaction in market.according to the basic conclusion of this trust model, the level of cooperation is determined by the formal institution $, which is an exogenous variable to the model. Therefore, the model fails to explain how the cooperation co-evolves with institutions, and what make the diversities of cooperate patterns in different economies. A significant shortcoming of this trust model is that it uses complete information and common knowledge assumptions. Actually, the common knowledge assumption underlies all of game theory and much of economic theory. For mathematics traceable equilibrium result, the structure of the game, the order of moves, the payoffs of others are supposed as common knowledge to all players. In a subjective modification framework, agent does not be fully aware of the cooperation threshold values of others. The agent decision is made based on the subjective brief acquired from learning or trial and error in the social interaction process. According to the behavior patterns implying by the trust model, one possible optional solution is that agent employs the 19

20 bounded-rational decision-making principle (Simon,1991), such as Rule of thumb or Satisficing Principle. For example, agent can classify others to several interaction categories, like family members, friends, casual acquaintances, and so on. In cases of encountering agents in close social relationships (lower social distance in the network of the model), he can make a good guess to the other s threshold value, and can make right choice between cooperation and defection correspondingly. Otherwise, the agent conceives the social average cooperative level and makes decision while meeting strangers accordingly. Under the random distribution of relationships and interactions 2, this behavior pattern could achieve a satisfactory result which approximate to the Pareto equilibrium in static analysis. 7 Social cooperation level T( ) Formal institution level T($) Social cooperation level Individual subjective beliefs Figure 6. A individual subjective belief form of social cooperation level Figure 6 illustrates the forming procedure of individual subjective belief on cooperation level. According to bounded rationality, individual cannot comprehend the complete information of all the other s trust threshold value. Instead, the average social cooperation threshold = R S ; and the formal institution level are used to establish a personal cooperation parameter in his subjective decision-making framework. The can be seen as a quasi-parameter in subjective analysis. According to Grief (2006), the quasi-parameter is defined as player s subjective expectation on the probability distribution of other player s types and strategies. In other words, it is the subjective belief on the actions of others in game. All players, observing the outcomes of the game, can develop only a subjective evaluation of the parameters and others strategies. In contrast to standard game model, since the approach makes weaker assumptions, its prediction power is, in general, weaker. For many applications, this immature approach represented in a less rigid mathematical formalization, however, it is significantly less demanding for the individual players, and in this sense it is more realistic. 2 The distribution of social relationships and interactions is more likely to be non-randomness in the real world. It s reasonable to assume that individuals in stronger social ties have higher possibility to encounter each other. However, an experimental simulation is more suitable for the cooperation analysis in that case. 20

21 A conceptual framework to express Hayek s Extended Order of Human Cooperation By modifying the trust game with subjective assumptions, a conceptual framework can be constructed to shed some light on Hayek s thoughts on the Spontaneous order. In this analysis, the Hayekian spontaneous order is regarded includes two aspects. First, the social cooperation threshold which is an endogenous solution generate by the trust game, can be seen as the informal institution. It actually reflects culture, traditions and norms related to trust and cooperation in social interactions. In Hayekian framework, it is important to understand the rise of the market by distinguishing between the evolution of instincts for cooperation, the cultural transmission of morals and the emergence of institutions supporting cooperation. In the static analysis of the trust model hereinbefore, the cooperation threshold and accordingly, the social trust and cooperation level is determined by the exogenous punishment on defections. Therefore, the informal and formal institutions are match in every moment of equilibrium. However, in a subjective framework, there may be two kinds of deviation between the formal and informal institutions. The first possible deviation is that the formal institution remains same, but the subjective beliefs of individuals change according to some norms transition. For example, cultural exchange with outside economy could effects the social trust and cooperation level of an economy. The second possible result is that subjective beliefs keep unchanged in a reform or revolution process of formal institution. This could happen because of bounded rationality of individual. They fail to recognize the real consequence of the ongoing formal institutional process. Either way, there is a deviation between informal and formal institutions. The average cooperation threshold value is an indicator of social trust and cooperation level. Second, formal institution which enforces punishment on defection behavior in social network also plays an important role in the evolution of spontaneous order. The progress in both directions of formal and informal institutions constitutes the Extended Order of Human Cooperation. The cooperate threshold on social relationships provide an indicator of social trust and cooperate preference. The entire vector of all threshold 7, or the average value of all threshold can be employed as a measure of culture, convention or informal institution on trust and cooperation in a society. According to the game model equilibrium analysis, cooperative level increase as the punishment of law enforced on defection. Therefore, informal institution is determined by formal institution in this stationary equilibrium model. 21

22 T( V ) T U ($) Figure 7. Cooperation order extended in two institutional aspects Figure 7 demonstrates idea of cooperation order extended in two institutional directions and the deviation of formal/informal institution. The vertical axis denoting T() is the informal institution of social trust and cooperation level; and the horizontal axis denoting T($) is the formal institution of punishment on defection behaviors. The joint progress in the two directions represents Hayekian extended order of human cooperation in economic market process. It is compatible to the globalization of market system that cooperation increases in both sense of social norms and the rule of law system. The curve in the middle of the figure indicates a possible institutional coevolution process path of an economy. When T()=T($), formal and informal institutions are perfect match in the static game model; otherwise, there is a deviation of formal/informal institution. Compare to the analysis of static model, deviations are regular phenomena in real world. However, there is constringency trend between informal and forma institutions because the gap between subjective decision-making beliefs and objective institutional structure could be filled with social learning and trial and error process in long run. 22

23 5. Comparative analysis of Cooperation patterns in China, Japan and the U.S. There are prevailing arguments that identify the East Asian developmental and institutional features with Confucianism, authoritarianism, collectivism and kinship-dominance, compared with Protestantism, democracy, individualism and the rule of law in the West(Aoki 2011). It is argued that these featured traditions had formed an unique trust and cooperate pattern based on relationships, or on the Differential Mode of Association in East Asian societies, such as China, Japan, Korea, Taiwan and overseas Chinese communities that sharing a heritage of Confucianism. In addition, it is believed that this behavior pattern has provided a social capital that gives East Asian a potential competitive advantage in global markets (Bian,1994,1997; Yang, 1994; Park and Luo, 2001; Gold et al., 2002). Relationships, known as Guanxi in China and Kankei in Japan provide a basis for the culture, business transactions and business operations. The trust game repeated in a social network shows an alternative to explain the interaction and the coevolution process of informal/formal institutions. Aiding with the conceptual subjective institutional analysis framework, it can be employed to analysis on the diversities of some realistic institution patterns. Based on the ideas from the framework built above, the difference of the conventions of cooperate patterns between the East, China and Japan as examples, and the West, such as US, are discussed as well as the formal institution system. Guanxi in China Guanxi in China has become a popular topic in both the academic and popular press. Guanxi refers to connections among individuals, which provide or imply the exchange of favors (Luo, 2001). These interpersonal relationships often form a vast relational network that is ubiquitous in all business dealings in China. Several empirical studies highlight the importance of guanxi. For example, Xin and Pearce (1996) found that executives of private companies developed and utilized guanxi more than executives of state-owned companies to compensate for the lack of formal institutional mechanisms. In a more recent study, Park and Luo (2001) found that institutional, strategic, and organizational factors were important antecedents to the use of guanxi in China. Moreover, Park and Luo found guanxi to be positively related to firm performance. Thus relationship building in China has been and continues to be an important topic for research. The term of guanxi is a Chinese phrase which generally refers to relationships or social connections based on mutual interests and benefits (Bian, 1994; Gold et al., 2002; Yang, 1994). Guanxi represents a way to bypass regulations, laws, or norms through personal connections with people who control limited resources. Guanxi being used as a special term to describe social relationships in Chinese implies the fact that there is a unique social interaction and cooperation pattern in China different from other societies. This view is compatible to the conception of the Differential Mode of Association. In From the Soil: the Foundation of Chinese Society (1947), Fei Hsiao-tung described China s problems in terms of the Chaxu geju (the Differential Mode of Association) and the 23